A fatal error occurred during a Windows Server Backup snap-in (Wbadmin.msc) operation.

Error details: The server threw an exception. 

Close Wbadmin.msc and then restart it.

For server 2012, 2012 r2, and 2016

1. Remove/backup the log files: C:\Windows\Logs\WindowsServerBackup
2. Uninstall the feature: “windows backup server”
3. Restart the Server
4. Restart again for good measure
5. Install the feature: “windows backup server”
6. Open Cmd (with admin rights) run (and answer yes): wbadmin delete catalog
7. Start the Backup Service
8. Recreate the backup Job and Services (as needed)

That should do it.